What if df/dt<0 for some t? Then the x coordinate will double back on itself... but you don't know what happens with the y coordinate. So your curve isn't the curve of a function (since it's multi-valued). Try drawing some curves like that and see if anything gets messed up

Office_Shredder:
Yes, that is another possiblity, :) Mine was only an example. What I am looking for is what happens when the curve "turns" back in one or more of the coordinates and when it exists in more than one quadrants and stuff like that. Anything that can go wrong. That is why I am asking these questions.